Your real problem is not in calculating the sensitivity and specificity, but
in calculating the confidence intervals for those values. To get sens. and
spec. you simply assume that the 10% sample of the test negatives is
representative of the 800 test negatives. Thus, the 20 false positives
represent 200 FPs and the 60 true negatives represent 600 TNs. Then sens. is
75 / (75+200) = 0.273; and spec. is 600 / (125+600) = 0.828. But the
confidence intervals calculated on these proportions will be too narrow,
because only 280 test results were confirmed, not all 1000. Offhand, I
cannot figure out a straight-forward way to calculate these confidence
intervals. Perhaps some statistician can tell us how this would be done. One
would hope that those who conducted this study would have consulted a
statistician before carrying out the study in this convenient but
complicated way.
David L. Doggett, Ph.D.
Senior Medical Research Analyst
Health Technology Assessment and Information Services
ECRI, a non-profit health services research organization
5200 Butler Pike
Plymouth Meeting, Pennsylvania 19462, U.S.A.
Phone: (610) 825-6000 x5509
FAX: (610) 834-1275
e-mail: [log in to unmask]
-----Original Message-----
From: Angela Boland [mailto:[log in to unmask]]
Sent: Friday, January 26, 2001 10:59 AM
To: [log in to unmask]
Subject: Specificity and sensitivity
Dear list members
Can anyone give advice for calculations regarding
specificity and sensitivity of a screening test? For
example, suppose that 1000 patients were screened. 200 were
tested positive and the remainder tested negative. Of the
200, 75 were found to be true positives and 125 were found
to be false positives. Of the 800 test negatives, a random
10% sample were further tested for the disease of whom 20
were found to be positive (ie false negatives) and 60 were
truly negative.
My question is: how do you calculate specificity and
sensitivity based on the fact that only 10% of the test
negatives were followed up?
All suggestions are appreciated.
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